1. Field of the Invention
This invention relates generally to geophysical exploration and in particular to a vibratory seismic source useful in geophysical exploration. More particularly, the invention relates to methods for using vibrators for seismic data acquisition.
2. Background Art
Seismic energy sources, including vibrators, are used in geophysical exploration on land and in water covered areas of the Earth. Acoustic energy generated by such sources travels downwardly into the Earth, is reflected from reflecting interfaces in the subsurface and is detected by seismic receivers, typically hydrophones or geophones, on or near the Earth's surface or water surface.
Generally, a seismic vibrator includes a base plate coupled to the water or land surface, a reactive mass, and hydraulic or other devices to cause vibration of the reactive mass and base plate. The vibrations are typically conducted through a range of frequencies in a pattern known as a “sweep” or “chirp.” Signals detected by the seismic receivers are cross correlated with a signal detected by a sensor disposed proximate the base plate. The result of the cross correlation is a seismic signal that approximates what would have been detected by the seismic receivers if an impulsive type seismic energy source had been used. An advantage provided by using vibrators for imparting seismic energy into the subsurface is that the energy is distributed over time, so that effects on the environment are reduced as compared to the environmental effects caused by the use of impulsive sources such as dynamite or air guns.
It is not only the possible environmental benefits of using vibrators that makes it desirable to use seismic vibrators in seismic surveying. By having a seismic energy source that can generate arbitrary types of seismic signals there may be substantial benefit to using more “intelligent” seismic energy signals than conventional sweeps or chirps. Such seismic energy sources would be able to generate signals have more of the characteristics of background noise, and thus be more immune to interference from noise, and at the same reduce their environmental impact.
A practical limit to using vibrators for such sophisticated signal schemes to operate marine vibrators in particular is the structure of marine vibrators known in the art. In order to generate arbitrary signals in the seismic frequency range it is necessary to have a source which has a high efficiency to make the source controllable within the whole seismic frequency range interest. Combining several vibrators that are individually controllable, with more sophisticated signal generating techniques would make it possible to generate seismic signals from several individual seismic energy sources at the same time that have a very low cross correlation, thereby making it possible to increase the efficiency of acquiring seismic data. Hydraulic marine vibrators known in the art typically have a resonance frequency that is higher than the upper limit of ordinary seismic frequencies of interest. This means that the vibrator energy efficiency will be relatively low, principally at low frequencies but generally throughout the seismic frequency range. Hydraulic marine vibrators can be difficult to control with respect to signal type and frequency content. Conventional marine seismic vibrators are also subject to strong harmonic distortion, which further limits the use of more complex driver signals. Such vibrator characteristics can be understood by examining the impedance for a low frequency vibrator.
The total impedance that will be experienced by a vibrator may be expressed as follows:Zr=Rr+jXr  (Eq. 1)wherein Zr is the total impedance, Rr is the radiation impedance, and Xr is the reactive impedance.
In an analysis of the energy transfer of a marine vibrator, the system including the vibrator and the water may be approximated as a baffled piston. The radiation impedance Rr of a baffled piston can be expressed as:Rr=πa2ρ0cR1(x)  (Eq. 2)and the reactive impedance can be expressed as:
                              X          r                =                  π          ⁢                                          ⁢                      a            2                    ⁢                      ρ            0                    ⁢          c          ⁢                                          ⁢                                    X              1                        ⁡                          (              x              )                                                          (                  Eq          .                                          ⁢          3                )                                where        ⁢                  :                                                                    x        =                              2            ⁢            k            ⁢                                                  ⁢            a                    =                                                    4                ⁢                π                ⁢                                                                  ⁢                a                            λ                        =                                          2                ⁢                ω                ⁢                                                                  ⁢                a                            c                                                          (                  Eq          .                                          ⁢          4                )                                                      R            1                    ⁡                      (            x            )                          =                  1          -                                    2              x                        ⁢                                          J                1                            ⁡                              (                x                )                                                                        (                  Eq          .                                          ⁢          5                )                                                      X            1                    ⁡                      (            x            )                          =                              4            π                    ⁢                                    ∫              0                              π                2                                      ⁢                                          sin                ⁡                                  (                                      x                    ⁢                                                                                  ⁢                    cos                    ⁢                                                                                  ⁢                    α                                    )                                            ⁢                              sin                2                            ⁢              α              ⁢                              ⅆ                α                                                                        (                  Eq          .                                          ⁢          6                )            in which ρ0 is the density of water, ω is the angular frequency, k is the wave number, a is the radius of the piston, c is the acoustic velocity, λ is the wave length, and J1 is a Bessel function of the first order.
Applying the Taylor series expansion to the above equations provides the expressions:
                                          R            1                    ⁡                      (            x            )                          =                                            x              2                                                      2                2                            ⁢                              1                !                            ⁢                              2                !                                              -                                    x              4                                                      2                4                            ⁢                              2                !                            ⁢                              3                !                                              +          …                                    (                  Eq          .                                          ⁢          7                )                                                      X            1                    ⁡                      (            x            )                          =                              4            π                    ⁡                      [                                          x                3                            -                                                x                  3                                                                      3                    2                                    ·                  5                                            +                                                x                  5                                                                      3                    2                                    ·                                      5                    2                                    ·                  7                                            -              …                        ]                                              (                  Eq          .                                          ⁢          8                )            
For low frequencies, when x=2ka is much smaller than 1, the real and imaginary part of the total impedance expression may be approximated with the first term of the Taylor series expansion. The expressions for low frequencies, when the wave length is much larger than the radius of the piston, become:
                                          R            1                    ⁡                      (            x            )                          →                              1            2                    ⁢                                    (              ka              )                        2                                              (                  Eq          .                                          ⁢          9                )                                                      X            1                    ⁡                      (            x            )                          ->                              8            ⁢            ka                                3            ⁢            π                                              (                  Eq          .                                          ⁢          10                )            
It follows that for low frequencies the radiation impedance R will be small as compared to the reactive impedance X, which suggests low efficiency signal generation. Accordingly, there is a need for efficient marine vibrators that can generate complex signals and there is a need to improve the time efficiency of operating seismic data acquisition to provide more economical operation and to minimize the environmental impact of marine seismic surveying.
There is also a need for seismic vibrator driver signals that can improve the efficiency with which equivalent signals to those generated by an impulsive seismic source may be recovered from a plurality of seismic vibrators operated substantially contemporaneously.